My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum


Thanks Tree1Thanks
  • 1 Post By Olinguito
Reply
 
LinkBack Thread Tools Display Modes
April 12th, 2014, 12:27 AM   #1
Member
 
Joined: Sep 2013

Posts: 84
Thanks: 2

Multiplicative inverse in factor ring?

Hello,
can someone tell me how to find the multiplicative inverse of an element in a factor ring?
Let the element be f and the factor ring T[x]/(m).
The basic idea is to solve a diophantine equation like f*u-m*v=1,right?and we need to find u
ricsi046 is offline  
 
April 12th, 2014, 04:03 AM   #2
Senior Member
 
Olinguito's Avatar
 
Joined: Apr 2014
From: Greater London, England, UK

Posts: 320
Thanks: 156

Math Focus: Abstract algebra
You have the right idea – except that an element of $T[x]/(m)$ is of the form $f+(m)$ where $f$ is a polynomial of degree at most $\deg(m)-1$. When you have found a polynomial $u$ such that $fu=1+mv$ for some polynomial $v$, the multiplicative inverse of $f+(m)$ will be $u+(m)$.
Thanks from ricsi046
Olinguito is offline  
April 12th, 2014, 04:05 AM   #3
Member
 
Joined: Sep 2013

Posts: 84
Thanks: 2

i see,thanks
ricsi046 is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
factor, inverse, multiplicative, ring



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
multiplicative inverse in modular arithmetic amnakhan786 Number Theory 1 November 19th, 2012 03:23 AM
multiplicative inverse using Euclids Algorithm mathslog Number Theory 7 May 25th, 2012 04:47 AM
Every member of a multiplicative group is its own inverse restin84 Number Theory 0 December 15th, 2011 11:11 AM
factor ring tinynerdi Abstract Algebra 3 May 21st, 2010 04:39 AM
Multiplicative inverse nightshadengale Number Theory 2 September 24th, 2007 07:42 PM





Copyright © 2019 My Math Forum. All rights reserved.